Chapter 5.2, Problem 66S

To determine

To solve the inequality:

  $3.6p<-4.5$

And to graph the solution on a number line.

Answer to Problem 66S

The solution of the inequality is $\left(-\infty ,-1.25\right)$ and corresponding correct option is d.

  

Explanation of Solution

Given:

  $3.6p<-4.5$

Concept Used:

• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Properties of inequality:
1. $b\le c\Rightarrow ab\le ac,\text{ if }a\ge 0$
2. $b\le c\Rightarrow ab\ge ac,\text{ if }a\le 0$

Calculation:

To solve the inequality:

  $3.6p<-4.5$

Divide both sides by 3.6:

  $\begin{array}{c}3.6p<-4.5\\ \frac{3.6p}{3.6}<\frac{-4.5}{3.6}\\ p<-1.25\end{array}$

Thus, the inequality is true for t less than $-1.25$ , thus the solution of given inequality in interval form is:

  $\left(-\infty ,-1.25\right)$

Now in order to sketch the graph of the solution of the inequality, since the interval of solution at right end point $-1.25$ is strict, so use a blank circle at $-1.25$ . And the solution interval has $-\infty$ at left endpoint which means every number less than from $-1.25$ to negative infinity is in the solution interval and does not contain the right end point in the number line. The graph of the inequality is shown below:

  

Hence, option d is correct.